In the literature, the study of persistence modules has been tackled mainly from two different perspectives. In the first works appeared in the literature about persistence theory, a dataset was encoded as a manifold, and the measurements on it as a Morse function on it. In this perspective, persistence can be grounded in Morse theory, with persistence modules determined by pairs of critical points of functions that give birth and death to a topological feature [1]}, [2]}, [3]}, [4]}. This paradigm has also a combinatorial counterpart developed for accelerating computations and based on discrete Morse theory [5]}, [6]}.
